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Operating modern power grids with stability guarantees is markedly important. Typical methods for analyzing and certifying power grid stability are largely centralized relying on the ability of the system operator to gather network-wide information and accurately compute the system's eigenvalues. These methods are oftentimes not privacy-preserving and computationally burdensome. They are therefore, not well-suited to modern power grids where small-signal stability has to be evaluated timely, efficiently and in a privacy-preserving fashion. In this paper, we introduce a distributed methodology for certifying small-signal stability of power grids and designing the local controllers. First, we analytically derive distributed conditions for network-wide stability that bus agents can inspect using local information. By leveraging these conditions, we then introduce a distributed control design algorithm (DCDA) that can guide the local control design so that stability of the interconnected system is guaranteed. The agents that adopt the proposed distributed algorithm are responsible for tuning their local controllers, producing their local control commands and ensuring that their local stability condition is met. The system operator is only responsible for verifying network-wide stability upon receiving affirmative responses from all agents and, announcing, that the overall system is stable. The proposed DCDA algorithm is numerically validated via simulations using the IEEE 39-bus system.

Recovering the distribution grid topology is essential to perform several distribution system operator functions. Many algorithms that address the topology recovery problem have already been proposed in the literature. Most are based on a priori information regarding which buses are fed by which substation; however, this information might not be available because frequent grid reconfigurations change the distribution grid portion connected to each substation. This paper addresses the problem of assigning every substation the set of buses that it is feeding, given field data. First, the aforementioned task is cast as a nonconvex optimization problem. Second, a relaxed version of the optimization problem is solved via the alternating direction method of multipliers. Finally, the performance of our approach is validated through numerical simulations of realistic scenarios using a standard IEEE benchmark feeder.

In this paper, a stochastic model is proposed for a joint statistical description of solar photovoltaic (PV) power and outdoor temperature. The underlying correlation emerges from solar irradiance that is responsible in part for both the variability in solar PV power and temperature. The proposed model can be used to capture the uncertainty in solar PV power and its correlation with the electric power consumption of thermostatically controlled loads. First, a model for solar PV power that explicitly incorporates the stochasticity due to clouds via a regime-switching process between the three classes of sunny , overcast and partly cloudy is proposed. Then, the relationship between temperature and solar power is postulated using a second-order Volterra model. This joint modeling is leveraged to develop a joint probabilistic forecasting method for solar PV power and temperature. Real-world datasets that include solar PV power and temperature measurements in California are analyzed and the effectiveness of the joint model in providing probabilistic forecasts is verified. The proposed forecasting methodology outperforms several reference methods thus portraying that the underlying correlation between temperature and solar PV power is well defined and only requires a simple lower-complexity sampling space.

Photovoltaic (PV) panels have become a significant source of electric power generation. These panels are considered to be one of the cleanest energy production systems available, so their spread is expected to increase in the following years, especially because recent technologies have reduced the cost of these panels. Unlike classic energy production methodologies that are connected to the high-voltage transmission power lines, many PV panels are connected directly to the lower voltage distribution networks of the electric power grid, making the management of the grid an ongoing challenge. In this letter, we address this challenge and show that the irradiance field that is required to calculate the expected power output of the PV panels can be estimated in a simplistic methodology, using partial observability of the solar radiation. We validate our proposed methodology by conducting an empirical study that uses real data of the solar radiation taken from satellites, and we show that even when the observability of the solar radiation is as low as 10% (meaning that only one in ten points of interest in a regular grid is observable), the irradiance field can be accurately estimated.

We present explicit sufficient conditions that guarantee the existence and uniqueness of the feasible load-flow solution for distribution networks with a generic topology (radial or meshed) modeled with positive sequence equivalents. In the problem, we also account for the presence of shunt elements. The conditions have low computational complexity and thus can be efficiently verified in a real system. Once the conditions are satisfied, the unique load-flow solution can be reached by a given fixed point iteration method of approximately linear complexity. Therefore, the proposed approach is of particular interest for modern active distribution network (ADN) setup in the context of real-time control. The theory has been confirmed through numerical experiments.

In this second part, we evaluate the performances of our control framework by applying it to a casestudy that contains a minimum set of elements allowing to show its applicability and potentials. Weshow how the computation of the PQt profiles, belief functions, and virtual costs can be synthesized forgeneric resources (i.e., dispatchable and stochastic generation systems, storage units, loads). The metricsof interest are: quality-of-service of the network represented by voltages magnitudes and lines currentmagnitudes in comparison with their operational boundaries; state-of-charge of electric and thermalstorage devices; proportion of curtailed renewables; and propensity of microgrid collapse in the case ofrenewables overproduction. We compare our method to two classic ones relying on droop control: thefirst one with only primary control on both frequency and voltage and the second one with an additionalsecondary frequency control operated by the slack device. We find that our method is able to indirectlycontrol the reserve of the storage systems connected to the microgrid, thus maximizing the autonomy inthe islanded operation and, at the same time, reducing renewables curtailment. Moreover, the proposedcontrol framework keeps the system in feasible operation conditions, better explores the various degreesof freedom of the whole system and connected devices, and prevents its collapse in case of extremeoperation of stochastic resources. All of these properties are obtained with a simple and generic controlframework that supports aggregation and composability.

Blackwell’s theory of approachability, introduced in 1956, has since proved a useful tool in the study of a range of repeated multiagent decision problems. Given a repeated matrix game with vector payoffs, a target set S is approachable by a certain player if he can ensure that the average payoff vector converges to that set, for any strategy of the opponent. In this paper we consider the case where a set need not be approachable in general, but may be approached if the opponent played favorably in some sense. In particular, we consider nonconvex sets that satisfy Blackwell’s dual condition, namely, can be approached when the opponent plays a stationary strategy. Whereas the convex hull of such a set is approachable, this is not generally the case for the original nonconvex set itself. We start by defining a sense of restricted play of the opponent (with stationary strategies being a special case), and then formulate appropriate goals for an opportunistic approachability algorithm that can take advantage of such restricted play as it unfolds during the game. We then consider a calibration-based approachability strategy that is opportunistic in that sense. A major motivation for this study comes from no-regret problems that lack a convex structure such as the problem of online learning with sample-path constraints, as formulated in Mannor et al. [Mannor S, Tsitsiklis JN, Yu JY (2009) Online learning with sample path constraints. J. Machine Learn. Res. 10:569–590]. Here the best-response-in-hindsight is not generally attainable, but only a convex relaxation thereof. Our proposed algorithm, while ensuring that relaxed goal, also comes closer to the nonrelaxed one when the opponent’s play is restricted in a well-defined sense.

We present sufficient conditions for the existence and uniqueness of load-flow solutions in three-phase distribution networks. The conditions can be efficiently verified for real distribution systems.

We propose a model-based learning algorithm, the Adaptive-resolution Reinforcement Learning (ARL) algorithm, that aims to solve the online, continuous state space reinforcement learning problem in a deterministic domain. Our goal is to combine adaptive-resolution approximation schemes with efficient exploration in order to obtain polynomial learning rates. The proposed algorithm uses an adaptive approximation of the optimal value function using kernel-based averaging, going from coarse to fine kernel-based representation of the state space, which enables us to use finer resolution in the "important" areas of the state space, and coarser resolution elsewhere. We consider an online learning approach, in which we discover these important areas online, using an uncertainty intervals exploration technique. In addition, we introduce an incremental variant of the ARL (IARL), which is a more practical version of the original algorithm with reduced computational complexity at each stage. Polynomial learning rates in terms of mistake bound (in a PAC framework) are established for these algorithms, under appropriate continuity assumptions.